I think there are many alternatives. You can use any positive answer...like: Persze. Természetesen. Hogyne. Mi az hogy. Naná. Bizony, etc...
And since ugye can follow a negative sentence, then you can use any negative answer.

But I am not sure what Zsanna meant by "typical (albeit a bit special) alternative"...

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Yes, your made-up dialogue makes that usage more natural to me. I just can't imagine replying "ház" only. Maybe if someone gets pissed off by being asked the same question (Ez ház, ugye?) the fifth time, he/she might shout at the other: "HÁZ!!!!"

I can imagine a lot of different situations where it could be said but I didn't want to go into long explanations about it before the OP actually asked for it. For me the point was that in Hungarian we tend to vary our answers in such a case (= positive answer to a Yes or No Question), instead of using the classical "yes" (igen).
It is another question (with quite a long answer) why we use and which in a particular case.

Francis, it is a speciality in Hungarian I am talking about, not a statistically most given answer - which we don't know. (In Italian it is not as typical as in Hungarian, although you are right, they don't always say "si", there is also "ecco" and others... still.)
For a language learner it is useful to see things "globally" as well as in its details.

... For a language learner it is useful to see things "globally" as well as in its details.

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Szia Zsanna! You are right (a hozzászólásom nem kritika akart lenni ...). What I wanted to say is that the general answer to questions with "ugye" is "igen". The other possibilities like "az/ház/igen, az" are rather alternatives for answering questions in Hungarian, not necessarily with "ugye", and they do not work automatically:

- Hárman vagytok, ugye?
- Az (absolutely wrong)

- Ez ház?
- Az (possible, even if no ugye is in the question)

As the original question is about answering "ugye", I think the other options may be misleading for a begginner, if they were understood as "universal" alternatives to "igen".

... it is a speciality in Hungarian I am talking about ...

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I agree, though it works also in some other languages, e.g. in Slovak (but this is not about "ugye").

Szia Zsanna! You are right (a hozzászólásom nem kritika akart lenni ...). What I wanted to say is that the general answer to questions with "ugye" is "igen". The other possibilities like "az/ház/igen, az" are rather alternatives for answering questions in Hungarian, not necessarily with "ugye", and they do not work automatically:

- Hárman vagytok, ugye?
- Az (absolutely wrong)

- Ez ház?
- Az (possible, even if no ugye is in the question)

As the original question is about answering "ugye", I think the other options may be misleading for a begginner, if they were understood as "universal" alternatives to "igen".

I agree, though it works also in some other languages, e.g. in Slovak (but this is not about "ugye").

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Ismét tökéletesen egyetértek. Javaslom, fogadjuk el ezt a választ a végsőnek.
I can't agree more again, I suggest taking this reply as the ultimate one. It has everything.

In case of yes/no probably not. From the point of view of Elemika's question/dilemma is important to underline that "ugye" cannot be repeated in the answer, because ugye [< úgy-e?) is a question itself.